OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Hypercube Graph
Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).
FORMULA
a(n) = 2^(n - 4)*n*(n - 1)*(n - 2)*(27*n - 79).
a(n) = 10*a(n-1) - 40*a(n-2) + 80*a(n-3) - 80*a(n-4) + 32*a(n-5).
G.f.: -6*x^3*(1 + 106*x)/(-1 + 2*x)^5.
MATHEMATICA
Table[Length[FindCycle[HypercubeGraph[n], {8}, All]], {n, 0, 9}]
Table[2^(n - 4) n (n - 1) (n - 2) (27 n - 79), {n, 0, 20}]
Table[3 2^(n - 3) Binomial[n, 3] (27 n - 79), {n, 0, 20}]
LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 0, 6, 696}, 20]
CoefficientList[Series[6 x^3 (1 + 106 x)/(1 - 2 x)^5, {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Aug 02 2023
STATUS
approved